Special prosecutors of the Republic of Korea investigating impeached President Park Geun-hye were denied permission to extend their probe and question her in person on Monday amid a graft scandal that threatens to topple her from office.

The special prosecutor's office will make its final indictments before its investigation into the scandal, which has engulfed the highest levels of politics and business in the country, closes on Tuesday, spokesman Lee Kyu-chul said.

The office of Prime Minister Hwang Kyo-ahn, acting as president since Park was impeached in December, said Hwang had rejected a request by prosecutors for a 30-day extension of their investigation.

"The special prosecutor's office regrets that the in-person questioning of the president could not happen and is deeply disappointed by the outcome," Lee said.

Prosecutors had sought to question Park as a suspect, he said.

ROK's main opposition parties threatened on Monday to impeach the country's acting leader after he refused to extend the investigation.

If successful, the impeachment of Hwang would rile the already tumultuous political landscape, putting another interim leader in power while the Constitutional Court decides the fate of both Hwang and Park.

Impeaching a prime minister requires support from half of the 299-member parliament. The three parties have a total of 166 seats, meaning they can easily reach the threshold to strip Hwang of power. But critics said the opposition parties must also consider the possibility of a strong backlash from conservatives if they make another high-profile impeachment effort.

The corruption scandal erupted last year over accusations that Park colluded with a friend, Choi Soon-sil, to pressure big businesses to donate to two foundations set up to back the president's policy initiatives.

The scandal has led to weekly protests by tens of thousands of people in the country.

Protesters hold placards reading "Impeach President Park Geun-hye!" in Seoul on Monday.Jung Yeonje/ Agence Francepresse